We consider the Cauchy problem for an $n\times n$ strictly hyperbolic system of balance laws $u_t+f(u)_x=g(x,u)$, $x\in\mathbb{R}$, $t>0$, $\|g(x,\cdot)\|_{\mathbf{C}^2}\leq\tilde{M}(x)\in\mathbf{L}^1$, endowed with the initial data $u(0,.)=u_o\in\mathbf{L}^1\cap\mathbf{BV}(\mathbb{R};\mathbb{R}^n)$. Each characteristic field is assumed to be genuinely nonlinear or linearly degenerate and nonresonant with the source, i.e., $|\lambda_i(u)|\geq c>0$ for all $i\in\{1,\dots,n\}$. Assuming that the $\mathbf{L}^1$ norms of $\|g(x,\cdot)\|_{\mathbf{C}^1}$ and $\|u_o\|_{\mathbf{BV}(\mathbb{R})}$ are small enough, we prove the existence and uniqueness of global entropy solutions of bounded total variation extending the result in [D.~Amadori, L.~Gosse, and G.~Guerra, {\it Arch.~Ration.~Mech.~Anal.}, 162 (2002), pp.~327--366] to unbounded (in $\mathbf{L}^\infty$) sources. Furthermore, we apply this result to the fluid flow in a pipe with discontinuous cross sectional area, showing existence and uniqueness of the underlying semigroup.
Guerra, G., Marcellini, F., & Schleper, V. (2009). Balance Laws with Integrable Unbounded Sources. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 41(3), 1164-1189.
Citazione: | Guerra, G., Marcellini, F., & Schleper, V. (2009). Balance Laws with Integrable Unbounded Sources. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 41(3), 1164-1189. |
Tipo: | Articolo in rivista - Articolo scientifico |
Carattere della pubblicazione: | Scientifica |
Titolo: | Balance Laws with Integrable Unbounded Sources |
Autori: | Guerra, G; Marcellini, F; Schleper, V |
Autori: | |
Data di pubblicazione: | 30-lug-2009 |
Lingua: | English |
Rivista: | SIAM JOURNAL ON MATHEMATICAL ANALYSIS |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1137/080735436 |
Appare nelle tipologie: | 01 - Articolo su rivista |
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